There are two primary ways of importing and exporting; 1) MySQL statements or 2) Comma Separated Values (CSV) translated into MySQL statements using the LOAD method.
This one is pretty straight forward unless you are exporting from a new PHPMyAdmin to an older version. If exporting to an older version you may have to specify compatibility. (i.e. from MySQL 5 to 4 you would use MySQL40). Otherwise it is pretty straight forward.
While MySQL statements are pretty straight forward, sometimes you want to manage the data in a table and make quick updates, or blanket changes. Using CSV, you can export tables to a program like excel, change the data, and then import. This process involves translating the SQL table data to CSV, opening in spreadsheet application of choice, manage data, output as CSV compatible with the PHP Load method, and then import back to your MySQL server.